songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Including critical points for Circles (maxima of spheres, restricted by a plane passing through the center)

This commit is contained in:
Pedro Machado Manhaes de Castro 2006-08-05 18:34:02 +00:00
parent e9b1d92d27
commit 9873a00bdb
1 changed files with 170 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

170
Algebraic_kernel_for_spheres/include/CGAL/Algebraic_kernel_for_spheres/internal_functions_on_roots_and_polynomials_2_3.h
View File

@ -149,6 +149,176 @@ namespace CGAL {
return res; return res;
} }
// ONLY the x is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
x_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqbc = CGAL::square(p.b()) + CGAL::square(p.c());
const FT sq_sum = sqbc + CGAL::square(p.a());
const FT delta = (sqbc * s.r_sq())/sq_sum;
return make_root_of_2(s.a(),i?-1:1,delta);
}
// ONLY the x is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
x_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c,
OutputIterator res)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqbc = CGAL::square(p.b()) + CGAL::square(p.c());
const FT sq_sum = sqbc + CGAL::square(p.a());
const FT delta = (sqbc * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.a(),-1,delta);
*res++ = make_root_of_2(s.a(),1,delta);
return res;
}
// ONLY the y is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
y_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqac = CGAL::square(p.a()) + CGAL::square(p.c());
const FT sq_sum = sqac + CGAL::square(p.b());
const FT delta = (sqac * s.r_sq())/sq_sum;
return make_root_of_2(s.b(),i?-1:1,delta);
}
// ONLY the y is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
y_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c,
OutputIterator res)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqac = CGAL::square(p.a()) + CGAL::square(p.c());
const FT sq_sum = sqac + CGAL::square(p.b());
const FT delta = (sqac * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.b(),-1,delta);
*res++ = make_root_of_2(s.b(),1,delta);
return res;
}
// ONLY the z is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
z_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqab = CGAL::square(p.a()) + CGAL::square(p.b());
const FT sq_sum = sqab + CGAL::square(p.c());
const FT delta = (sqab * s.r_sq())/sq_sum;
return make_root_of_2(s.c(),i?-1:1,delta);
}
// ONLY the z is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
z_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c,
OutputIterator res)
{
typedef typename AK::FT FT;
typedef typename AK::Root_of_2 Root_of_2;
typedef typename AK::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename AK::Polynomial_for_spheres_2_3 Polynomial_for_spheres_2_3;
typedef typename AK::Polynomial_1_3 Polynomial_1_3;
const Polynomial_for_spheres_2_3 &s = c.first;
const Polynomial_1_3 &p = c.second;
// It has to be the equation of a diametral circle
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
const FT sqab = CGAL::square(p.a()) + CGAL::square(p.b());
const FT sq_sum = sqab + CGAL::square(p.c());
const FT delta = (sqab * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.c(),-1,delta);
*res++ = make_root_of_2(s.c(),1,delta);
return res;
}
} // namespace AlgebraicSphereFunctors } // namespace AlgebraicSphereFunctors
} // namespace CGAL } // namespace CGAL